Device and method for training a polyhedral classifier

Abstract

A method for training a polyhedral classifier is described including obtaining training data in a data space, the training data including first data points associated with a first label and second data points associated with a second label, determining a pair of hyperplanes by determining an orientation of the pair of hyperplanes based on a minimization of a distance between the pair of hyperplanes such that the first data points lie between the hyperplanes in relation to a distance between the pair of hyperplanes such that both the first data points and the second data points lie between the hyperplanes and determining the position of the pair of hyperplanes such that the first data points lie between the pair of hyperplanes and the second data points are at least partially separated from the first data points by the pair of hyperplanes.

What is claimed is: 
     
       1. A method for training a polyhedral classifier for classifying objects in an image, comprising the following steps:
 obtaining training data in a data space, the training data including a plurality of first data points associated with a first label and a plurality of second data points associated with a second label, the training data being based on the image, the first label represents a classification concerning whether an object is present in at least part of the image or not; and 
 determining a pair of parallel hyperplanes by:
 determining an orientation of the pair of parallel hyperplanes based on a minimization of a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that the plurality of first data points lie between the pair of parallel hyperplanes in relation to a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that both the plurality of first data points and the plurality of second data points lie between the pair of parallel hyperplanes; and 
 determining a position of the pair of parallel hyperplanes such that the plurality of first data points lie between the pair of parallel hyperplanes and the plurality of second data points are at least partially separated from the plurality of first data points by the pair of parallel hyperplanes, wherein: 
 the polyhedral classifier belongs to a driving assistance system included in a vehicle and is trained to classify input sensor data provided by at least one sensor of the vehicle, 
 the driving assistance system is configured to control the vehicle based on the input sensor data classified by the polyhedral classifier, and 
 the pair of parallel hyperplanes are used for determining the classification and belong to the polyhedral classifier. 
 
 
     
     
       2. The method of  claim 1 , wherein the relation is a ratio of: the distance between the pair of parallel hyperplanes such that the plurality of first data points lie between the pair of parallel hyperplanes, and the distance between the pair of parallel hyperplanes such that both the plurality of first data points and the plurality of second data points lie between the pair of parallel hyperplanes. 
     
     
       3. The method of  claim 1 , wherein the determining of the pair of parallel hyperplanes includes determining a representation of a linear function mapping the data space to real numbers which gives the orientation of the pair of parallel hyperplanes and an interval whose endpoints give the position of the pair of parallel hyperplanes in the data space. 
     
     
       4. The method of  claim 3 , wherein the distance between the pair of the hyperplanes is given by a length of the interval. 
     
     
       5. The method of  claim 1 , wherein the obtaining of the training data in the data space includes mapping an original set of training data points in an original data space to the data space using a transformation mapping from the original data space to the data space, wherein the transformation mapping is configured to map the original data space to a boundary of a strictly convex set in the data space, and wherein the original data space and the data space are Euclidean spaces and a dimension of the data space is higher than a dimension of the original data space. 
     
     
       6. The method of  claim 5 , wherein the dimension of the data space is higher than the dimension of the original data space by one. 
     
     
       7. The method of  claim 5 , wherein the transformation mapping is configured to map the original data space to a sphere in the data space. 
     
     
       8. The method of  claim 1 , further comprising the following step:
 removing, those of the second data points which do not lie between the determined pair of parallel hyperplanes, from the training data. 
 
     
     
       9. The method of  claim 1 , further comprising the following step:
 determining a sequence of pairs of parallel hyperplanes separating the plurality of first data points from the plurality of second data points, the determining including, for each of the pairs of parallel hyperplanes of the sequence:
 determining an orientation of the pair of parallel hyperplanes of the sequence based on a minimization of a distance between the pair of parallel hyperplanes of the sequence that the pair of parallel hyperplanes of the sequence need to have such that the plurality of first data points lie between the pair of parallel hyperplanes of the sequence in relation to a distance between the pair of parallel hyperplanes of the sequence that the pair of parallel hyperplanes of the sequence need to have such that both the plurality of first data points and the plurality of second data points not yet separated from the plurality of first data points by a preceding pair of parallel hyperplanes of the sequence lie between the pair of parallel hyperplanes of the sequence; and 
 determining a position of the pair of parallel hyperplanes of the sequence such that the plurality of first data points lie between the pair of parallel hyperplanes of the sequence and the plurality of second data points are at least partially separated from the plurality of first data points by the pair of parallel hyperplanes of the sequence. 
 
 
     
     
       10. The method of  claim 1 , wherein determining the orientation of the pair of parallel hyperplanes includes selecting a candidate orientation and improving the orientation in a course of one or more orientation search iterations. 
     
     
       11. The method of  claim 10 , wherein the candidate orientation is selected to separate at least one second data point from the plurality of first data points. 
     
     
       12. The method of  claim 10 , wherein selecting the candidate orientation includes randomly selecting a second data point from the plurality of second data points and determining the candidate orientation to separate at least the selected second data point from the plurality of first data points. 
     
     
       13. A classifier training device configured to train a polyhedral classifier for classifying objects in an image, the classifier training device configured to:
 obtain training data in a data space, the training data including a plurality of first data points associated with a first label and a plurality of second data points associated with a second label, the training data being based on the image, the first label represents a classification concerning whether an object is present in at least part of the image or not; and 
 determine a pair of parallel hyperplanes by:
 determining an orientation of the pair of parallel hyperplanes based on a minimization of a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that the plurality of first data points lie between the pair of parallel hyperplanes in relation to a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that both the plurality of first data points and the plurality of second data points lie between the pair of parallel hyperplanes; and 
 determining a position of the pair of parallel hyperplanes such that the plurality of first data points lie between the pair of parallel hyperplanes and the plurality of second data points are at least partially separated from the plurality of first data points by the pair of parallel hyperplanes, wherein: 
 the polyhedral classifier belongs to a driving assistance system included in a vehicle and is trained to classify input sensor data provided by at least one sensor of the vehicle, 
 the driving assistance system is configured to control the vehicle based on the input sensor data classified by the polyhedral classifier, and 
 the pair of parallel hyperplanes are used for determining the classification and belong to the polyhedral classifier. 
 
 
     
     
       14. A non-transitory machine-readable storage medium on which is stored program instructions for training a polyhedral classifier for classifying objects in an image, the program instructions, when executed by one or more processors, causing the one or more processor to perform:
 obtaining training data in a data space, the training data including a plurality of first data points associated with a first label and a plurality of second data points associated with a second label, the training data being based on the image, the first label represents a classification concerning whether an object is present in at least part of the image or not; and 
 determining a pair of parallel hyperplanes by:
 determining an orientation of the pair of parallel hyperplanes based on a minimization of a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that the plurality of first data points lie between the pair of parallel hyperplanes in relation to a distance between the pair of parallel hyperplanes that the pair of parallel hyperplanes need to have such that both the plurality of first data points and the plurality of second data points lie between the pair of parallel hyperplanes; and 
 determining a position of the pair of parallel hyperplanes such that the plurality of first data points lie between the pair of parallel hyperplanes and the plurality of second data points are at least partially separated from the plurality of first data points by the pair of parallel hyperplanes, wherein: 
 the polyhedral classifier belongs to a driving assistance system included in a vehicle and is trained to classify input sensor data provided by at least one sensor of the vehicle, 
 the driving assistance system is configured to control the vehicle based on the input sensor data classified by the polyhedral classifier, and 
 the pair of parallel hyperplanes are used for determining the classification and belong to the polyhedral classifier.